The invention generally relates to methods of fabrication of micro-optics devices such as vertical microcavities. More particularly, it concerns methods of fabrication of micro-optics with embedded defects for enhancing electromagnetic wave confinement.
Micro-optics devices such as optical microcavities are known to confine light to a small volume. Devices using optical microcavities are today essential in many fields, ranging from optoelectronics to quantum information. Typical applications are long-distance data transmission over optical fibers and read/write laser beams in DVD/CD players. A variety of confining semiconductor microstructures has been developed and studied, involving various geometrical and resonant properties. A “microcavity” (hereafter MC) has smaller dimensions than a conventional optical cavity; its dimensions are often only a few micrometers and it may comprise parts that can even reach the nanometer range. Such dimensions notably allow for studying and harnessing quantum effects of electromagnetic fields.
More specifically, a Fabry-Perot-like cavity or a MC forms an optical cavity or resonator, which allows for a standing wave to form inside the spacer layer. The thickness of the latter determines the “cavity-modes”, which correspond to the wavelengths and field distributions that can be transmitted and forms as standing wave inside the resonator. An ideal cavity would confine light indefinitely (that is, without loss) and would have resonant frequencies at defined values. The deviations from this ideal paradigm are either intentional (e.g., outcoupling) or due to design or fabrication related limitations or imperfections (e.g., scattering). They are captured by the cavity Q factor, which is proportional to the confinement time in units of the optical period. Another important descriptive parameter is the effective mode volume (V), which relates to the number of optical modes present in the cavity. In general, the realization of practical devices requires maximizing the ratio Q/V, i.e., high values for Q and low values for V are important to increase light-matter interactions in processes such as spontaneous emission, nonlinear optical processes and strong coupling.
The quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is. The value of Q is usually defined as 2π×the total energy stored in the structure, divided by the energy lost in a single oscillation cycle. In optics, and more generally for high values of Q, the following definition can be retained:
                              Q          =                                                    f                r                                            Δ                ⁢                                                                  ⁢                f                                      =                                          ω                r                                            Δ                ⁢                                                                  ⁢                ω                                                    ,                            (        1        )            
where fr is the resonant frequency, Δf is the bandwidth, ωr=2πfr is the angular resonant frequency, and Δω is the angular bandwidth. A cavity providing a larger Q confines the photons for a longer time.
The definition of the effective mode volume is, in the literature, usually inspired from Purcell effect calculations, giving rise to:
                                          V            eff                    =                                    ∫                                                ɛ                  ⁡                                      (                    r                    )                                                  ⁢                                                                                                E                      ⁡                                              (                        r                        )                                                                                                  2                                ⁢                                  ⅆ                                      r                    3                                                                                                      ɛ                ⁡                                  (                                      r                                          ma                      ⁢                                                                                          ⁢                      x                                                        )                                            ⁢                              max                ⁡                                  (                                                                                                          E                        ⁡                                                  (                          r                          )                                                                                                            2                                    )                                                                    ,                            (        2        )            
where:
∈(r) is the dielectric constant as a function of the spatial coordinate r,
rmax is the location of the maximum squared electric field,
|E(r)| is the electric field strength at the spatial coordinate r, and
V is a quantization volume encompassing the resonator and with a boundary in the radiation zone of the cavity mode under study.
Eq. (2) gives the spatial intensity enhancement factor at the point of maximum electric field intensity inside a 3D structure. However, in some cases it is more important to estimate the mode distribution or “light-confining” ability of a structure. Thus, simulations in a 2D domain may be adequate in this case. The modal volume would then be obtained by integrating over the relevant 2D surface, as provided e.g., by the Software “Meep” (or MEEP), i.e., a finite-difference time-domain (FDTD) simulation software package to model electromagnetic systems. The resulting value of V does accordingly not compare directly with values as usually reported in the literature with 3D calculation. It is nonetheless sufficient, together with the electric field pattern, for comparing the light confining abilities of simulated structures. On the contrary, Q remains as defined in Eq. (1).
A strong confinement of photons in an ultra-small cavity (with dimensions of the order of optical wavelengths) is important for the development of nanophotonic applications, such as single-photon sources, ultralow-threshold (polariton) lasers, optical filters and optical switch.
As indicated above, Q determines how long photons can be confined in a cavity. In the weak light-matter coupling regime, the spontaneous emission rate of the emitter inside a cavity is enhanced by the Purcell effect, whereby Q/V is to be maximized. On the other hand, in the strong light-matter coupling regime, the value of Q/V1/2 is to be maximized, which is closely related to the ratio Q/V. Therefore, as a general rule, the value of Q/V is an important measure of the light confinement ability of a cavity.
Next, beyond Q and V, other issues to consider for the fabrication of microcavities are the fabrication complexity, structure tolerance, incorporation of active (quantum) emitters, in-coupling and out-coupling of light, and practicality of electrical contacting. For devices such as studied here, the conventional technology of vertical-cavity surface-emitting laser, or VCSEL, can be used. For other microcavities, other contact methods are known per se.
In vertical microcavity structures, there are essentially two ways of achieving lateral confinement, either by realizing a micropost (or micropillar) or a lateral aperture. Such structures usually offer small cavity volume and relatively high Q. They have emission patterns that particularly suited for coupling emitted photons, e.g., with optical fibers. They can further incorporate quasi-atomic quantum dots as emitters. Typically, in such structures, a confinement region is comprised between two mirrors, such as to provide one dimension (vertical) of cavity confinement. The lateral (in-plane) confinement is provided by air-dielectric guiding by total internal reflection (in the case of a micropost) or by a metal or oxide aperture. The minors consist of distributed Bragg reflectors (or DBRs), i.e., structures which are formed from multiple layers of alternating materials (layer pairs) with varying refractive index or by periodic variation of some dimensional characteristics (e.g., the height) of a dielectric waveguide, resulting in periodic variation in the effective refractive index in the guide. Each layer boundary causes a partial reflection of an optical wave.
There are different means of fabricating MCs. A common method of fabrication consists of evaporating alternate layers of dielectric media to form the mirrors and the medium inside the spacer layer, e.g., using molecular beam epitaxy (MBE).
In order to reduce the mode volume of a vertical MC, the usual approach consists of etching a planar MC into a micropillar. High Q values (˜105) have been demonstrated for large diameter III-V pillars, resulting in a large mode volume (V>50(λ/n)3), where λ is the wavelength and n the refractive index, see e.g., Reitzenstein et al., Appl. Phys. Lett. 90, 251109 (2007). However, small values of V are crucial for applications in cavity quantum electrodynamics (cQED) since the light-matter coupling strength is proportional to V−1/2 in this case. Small V can be achieved by reducing the pillar diameter. This, however, leads to significant reduction of Q due to side wall roughness and fabrication difficulties. Also, it is difficult to have single emitters located at the cavity antinodes in this case.
El Daif, et al. have proposed a MBE-grown III-V semiconductor (GaAs, AlGaAs, InGaAs) microcavity, see Appl. Phys. Lett. 88, 061105 (2006) and U.S. Pat. No. 7,729,043 B2. Before the deposition of the top DBR, one part of the cavity region is raised or recessed by using lithography and chemical etching. Such a raised portion essentially forms a square or rectangle pattern (side view). Because of the altered cavity length is determined by the region comprising the raised portions, light is also confined laterally in such cavities. However, it can be realized that the square-shaped pattern introduces significant light scattering, which in turn impacts the Q/V value (as to be discussed later in details). Also, the cavity length is changed within the spacer: the lithography/etching process required for achieving such structures is not compatible with many materials.
In general, “lithography” concerns processes for producing patterns of (essentially) two dimensional shapes, such as, for example, a resist coated on a semiconductor device. Conventional photolithography (optical lithography) is running into problems when the feature size is reduced, e.g. below 45 nm. These problems arise from fundamental issues such as sources for the short wavelength of light, photoresist collapse, lens system quality for short wavelength light and masks cost. To overcome such issues, alternative approaches have been explored.
Examples of alternative approaches are provided by nanolithography techniques, which can be seen as high resolution patterning of surfaces. More precisely, nanolithography refers to fabrication techniques of nanometer-scale structures. Depending on the actual technique used, patterns may be obtained which have one dimension between the size of an individual atom and approximately 100 nm (hence partly overlapping with photolithography). Such techniques further include charged-particle lithography (ion- or electron-beams), nanoimprint lithography and its variants, and scanning probe lithography (SPL) (for patterning at the nanometer-scale). SPL is for instance described in detail in Chemical Reviews, 1997, Volume 97 pages 1195 to 1230, “Nanometer-scale Surface Modification Using the Scanning Probe microscope: Progress since 1991”, Nyffenegger et al. and the references cited therein.
In general, SPL is used to describe lithographic methods wherein a probe tip is moved across a surface to form a pattern. Scanning probe lithography makes use of scanning probe microscopy (SPM) techniques. SPM techniques rely on scanning a probe, e.g. a sharp tip, in close proximity with a sample surface whilst controlling interactions between the probe and surface. A confirming image of the sample surface can afterwards be obtained, typically using the same scanning probe in a raster scan of the sample. In the raster scan either the probe-surface interaction or the tip-surface distance controlled to keep the interaction constant is recorded as a function of position and images are produced as a two-dimensional grid of data points.
The lateral resolution achieved with SPM varies with the underlying technique: atomic resolution can be achieved in some cases. Use can be made of piezoelectric actuators to execute scanning motions with a precision and accuracy at any desired length scale, up to (or even better than) the atomic scale. The two main types of SPM are the scanning tunneling microscopy (STM) and the atomic force microscopy (AFM). In the following, acronyms STM/AFM may refer to either the microscopy technique or to the corresponding microscope itself.
In particular, the AFM is a device in which the topography of a sample is modified or sensed by a probe mounted on the end of a cantilever. As the sample is scanned, interactions between the probe and the sample surface cause pivotal deflection of the cantilever. The topography of the sample may thus be determined by detecting or controlling this deflection of the probe. Yet, by manipulating the tip-surface interaction, the surface topography may be modified to produce a pattern on the sample.
Following this idea, in a SPL device, a probe is scanned across a functional surface and brought to locally interact with the functional material. The most common approach relies on a local anodic oxidation of e.g., a silicon substrate using a conductive tip and a defined tip-sample voltage. In the presence of water, an oxide is formed beneath the tip which can be exploited for further patterning steps. Another approach is thermomechanical indentation, i.e., interaction with the probe causes material on the surface to be removed or deformed, shaped, etc. However, the use of SPL probes for nanopatterning applications is still under development.